A stochastic daily mean temperature model for weather derivatives

Weather derivatives are usually priced by analyzing the climatologic data of an underlying weather index. This research proved that when using temperature as an underlying weather index that climatology was not fully representative of future outcomes. Weather derivative contracts based on temperature are measured by degree days, which are a metric of energy consumption. Previous research attempted to develop techniques to model degree days, but these techniques were based on invalid statistical assumptions and lacked robustness. Due to the fact that degree days are an aggregate monthly metric and path dependent, it was important to model the complete behavior of a time series by simulating the daily mean temperature.

This research provided an in depth statistical analysis of the daily mean temperature time series for eighteen cities from the Chicago Mercantile Exchange (CME). The residuals, which represented the difference between the observed data and trend, were used to develop two models to simulate a possible temperature time series for 2007. A distribution of ten thousand possible outcomes were created for each model, and then analyzed against the climatologic data sets. Ultimately, this research exhibited that statistics extracted from the analysis of the residuals could be simulated to produce realistic outcomes of degree days for weather derivative contracts.